The table below will focus on unilateral and bilateral ztransforms.
When given a signal (or sequence), the table can be very useful
in finding the corresponding ztransform. The table also
specifies the region of
convergence, which allows us to pick out the unilateral
and bilateral transforms.
The notation for z z found in the
table below may differ from that found in other tables. For
example, the basic ztransform of
un
u
n
can be written as either of the following two
expressions, which are equal:
zz−1=11−z1
z
z
1
1
1
z
1
(1)
Table 1
Signal 
ZTransform 
ROC 
δn−k
δ
n
k

z−k
z
k

Allz
All
z

un
u
n

zz−1
z
z
1

z>1
z
1

−u(−n)−1
u
n
1

zz−1
z
z
1

z<1
z
1

nun
n
u
n

zz−12
z
z
1
2

z>1
z
1

n2un
n
2
u
n

z(z+1)z−13
z
z
1
z
1
3

z>1
z
1

n3un
n
3
u
n

z(z2+4z+1)z−14
z
z
2
4
z
1
z
1
4

z>1
z
1

(−αn)u(−n)−1
α
n
u
n
1

zz−α
z
z
α

z<α
z
α

αnun
α
n
u
n

zz−α
z
z
α

z>α
z
α

nαnun
n
α
n
u
n

αzz−α2
α
z
z
α
2

z>α
z
α

n2αnun
n
2
α
n
u
n

αz(z+α)z−α3
α
z
z
α
z
α
3

z>α
z
α

∏
k
=1mn−k+1αmm!αnun
k
1
m
n
k
1
α
m
m
α
n
u
n

zz−αm+1
z
z
α
m
1

γncosαnun
γ
n
α
n
u
n

z(z−γcosα)z2−(2γcosα)z+γ2
z
z
γ
α
z
2
2
γ
α
z
γ
2

z>α
z
α

γnsinαnun
γ
n
α
n
u
n

zγsinαz2−(2γcosα)z+γ2
z
γ
α
z
2
2
γ
α
z
γ
2

z>α
z
α
